# load packages
library(prioritizr)
## Loading required package: raster
## Loading required package: sp
## Loading required package: proto
library(prioritizrdata)
# import data
data(tas_pu, package = "prioritizrdata")
data(tas_features, package = "prioritizrdata")
# add locked_out field
tas_pu$locked_out <- tas_pu$cost < quantile(tas_pu$cost, 0.2)[[1]]
tas_pu$locked_out <- tas_pu$locked_out & (!tas_pu$locked_in)
# set budget
budget <- ceiling(sum(tas_pu$cost[tas_pu$locked_in]) +
sum(tas_pu$cost[!tas_pu$locked_in]) * 0.1)
print(budget)
## [1] 10469
spplot(tas_pu, "cost", main = NULL, colorkey = TRUE)
spplot(tas_pu, "locked_in", col.regions = c("grey90", "#01AE6E"), main = NULL,
colorkey = FALSE)
spplot(tas_pu, "locked_out", col.regions = c("grey90", "#00195B"), main = NULL,
colorkey = FALSE)
# create problem
p <- problem(tas_pu, tas_features, "cost") %>%
add_min_set_objective() %>%
add_relative_targets(0.1) %>%
add_binary_decisions() %>%
add_gurobi_solver(gap = 0)
# solve problem
s <- solve(p)
## Optimize a model with 62 rows, 1130 columns and 1560 nonzeros
## Variable types: 0 continuous, 1130 integer (1130 binary)
## Coefficient statistics:
## Matrix range [1e-02, 7e-01]
## Objective range [2e-01, 6e+01]
## Bounds range [1e+00, 1e+00]
## RHS range [2e-03, 2e+00]
## Found heuristic solution: objective 2923.44
## Presolve removed 7 rows and 324 columns
## Presolve time: 0.01s
## Presolved: 55 rows, 806 columns, 1474 nonzeros
## Found heuristic solution: objective 1861.8029484
## Variable types: 0 continuous, 806 integer (806 binary)
## Presolved: 55 rows, 806 columns, 1474 nonzeros
##
##
## Root relaxation: objective 1.109977e+03, 81 iterations, 0.00 seconds
##
## Nodes | Current Node | Objective Bounds | Work
## Expl Unexpl | Obj Depth IntInf | Incumbent BestBd Gap | It/Node Time
##
## 0 0 1109.97666 0 45 1861.80295 1109.97666 40.4% - 0s
## H 0 0 1409.5043990 1109.97666 21.3% - 0s
## H 0 0 1368.3389336 1109.97666 18.9% - 0s
## 0 0 1191.69516 0 67 1368.33893 1191.69516 12.9% - 0s
## H 0 0 1297.5501015 1191.69516 8.16% - 0s
## H 0 0 1291.3683105 1191.69516 7.72% - 0s
## 0 0 1203.70019 0 77 1291.36831 1203.70019 6.79% - 0s
## 0 0 1204.92263 0 80 1291.36831 1204.92263 6.69% - 0s
## 0 0 1205.14029 0 81 1291.36831 1205.14029 6.68% - 0s
## 0 0 1205.14497 0 82 1291.36831 1205.14497 6.68% - 0s
## 0 0 1224.66347 0 69 1291.36831 1224.66347 5.17% - 0s
## 0 0 1226.17222 0 87 1291.36831 1226.17222 5.05% - 0s
## 0 0 1226.79040 0 91 1291.36831 1226.79040 5.00% - 0s
## 0 0 1226.80150 0 90 1291.36831 1226.80150 5.00% - 0s
## 0 0 1239.58613 0 79 1291.36831 1239.58613 4.01% - 0s
## 0 0 1240.29587 0 89 1291.36831 1240.29587 3.95% - 0s
## 0 0 1240.97346 0 90 1291.36831 1240.97346 3.90% - 0s
## 0 0 1241.21034 0 90 1291.36831 1241.21034 3.88% - 0s
## 0 0 1243.42366 0 91 1291.36831 1243.42366 3.71% - 0s
## 0 2 1243.56246 0 91 1291.36831 1243.56246 3.70% - 0s
## H 510 372 1289.3775737 1251.09811 2.97% 14.4 1s
## H 510 353 1287.1387837 1251.09811 2.80% 14.4 1s
## H 512 337 1287.0824807 1251.09811 2.80% 14.3 1s
## H 736 357 1274.4088496 1258.77234 1.23% 18.8 2s
## H 993 337 1272.3312691 1261.23389 0.87% 20.0 2s
## H 1126 318 1272.2062879 1261.89447 0.81% 20.4 2s
## H 1272 251 1270.4058038 1263.23901 0.56% 20.2 2s
## H 1474 261 1270.2357945 1264.13028 0.48% 19.7 2s
## H 1478 263 1270.1750559 1264.23280 0.47% 19.7 2s
## * 2157 277 32 1270.0595355 1266.70987 0.26% 19.3 3s
## * 2595 213 33 1269.8912984 1267.74529 0.17% 18.6 4s
##
## Cutting planes:
## Gomory: 2
## Cover: 47
## MIR: 68
## StrongCG: 29
## Flow cover: 48
## Zero half: 8
##
## Explored 2997 nodes (52771 simplex iterations) in 4.36 seconds
## Thread count was 1 (of 4 available processors)
##
## Solution count 10: 1269.89 1270.06 1270.18 ... 1287.14
##
## Optimal solution found (tolerance 0.00e+00)
## Best objective 1.269891298423e+03, best bound 1.269891298423e+03, gap 0.0000%
# plot solution
spplot(s, "solution_1", col.regions = c("grey90", "#D81E36"), main = NULL,
colorkey = FALSE)
# create problem
p <- problem(tas_pu, tas_features, "cost") %>%
add_min_set_objective() %>%
add_relative_targets(0.1) %>%
add_locked_in_constraints("locked_in") %>%
add_binary_decisions() %>%
add_gurobi_solver(gap = 0)
# solve problem
s <- solve(p)
## Optimize a model with 62 rows, 1130 columns and 1560 nonzeros
## Variable types: 0 continuous, 1130 integer (1130 binary)
## Coefficient statistics:
## Matrix range [1e-02, 7e-01]
## Objective range [2e-01, 6e+01]
## Bounds range [1e+00, 1e+00]
## RHS range [2e-03, 2e+00]
## Found heuristic solution: objective 9887.26
## Presolve removed 33 rows and 834 columns
## Presolve time: 0.00s
## Presolved: 29 rows, 296 columns, 535 nonzeros
## Found heuristic solution: objective 9049.6721583
## Variable types: 0 continuous, 296 integer (296 binary)
## Presolved: 29 rows, 296 columns, 535 nonzeros
##
##
## Root relaxation: objective 8.927880e+03, 43 iterations, 0.00 seconds
##
## Nodes | Current Node | Objective Bounds | Work
## Expl Unexpl | Obj Depth IntInf | Incumbent BestBd Gap | It/Node Time
##
## 0 0 8927.88005 0 17 9049.67216 8927.88005 1.35% - 0s
## H 0 0 8960.0146241 8927.88005 0.36% - 0s
## H 0 0 8953.9351080 8927.88005 0.29% - 0s
## H 0 0 8951.8757990 8927.88005 0.27% - 0s
## H 0 0 8941.5553815 8927.88005 0.15% - 0s
## 0 0 8938.29590 0 14 8941.55538 8938.29590 0.04% - 0s
## 0 0 8938.29590 0 12 8941.55538 8938.29590 0.04% - 0s
## 0 0 8938.67268 0 15 8941.55538 8938.67268 0.03% - 0s
## 0 0 8938.67268 0 8 8941.55538 8938.67268 0.03% - 0s
## 0 0 8939.37776 0 12 8941.55538 8939.37776 0.02% - 0s
## 0 0 8939.37776 0 8 8941.55538 8939.37776 0.02% - 0s
## H 0 0 8940.7420726 8939.37776 0.02% - 0s
## 0 0 8939.49854 0 11 8940.74207 8939.49854 0.01% - 0s
## 0 0 8940.65762 0 2 8940.74207 8940.65762 0.00% - 0s
##
## Cutting planes:
## Cover: 6
## MIR: 1
##
## Explored 1 nodes (178 simplex iterations) in 0.05 seconds
## Thread count was 1 (of 4 available processors)
##
## Solution count 7: 8940.74 8941.56 8951.88 ... 9467.37
##
## Optimal solution found (tolerance 0.00e+00)
## Best objective 8.940742072619e+03, best bound 8.940742072619e+03, gap 0.0000%
# plot solution
spplot(s, "solution_1", col.regions = c("grey90", "#D81E36"), main = NULL,
colorkey = FALSE)
# create problem
p <- problem(tas_pu, tas_features, "cost") %>%
add_min_set_objective() %>%
add_relative_targets(0.1) %>%
add_locked_in_constraints("locked_in") %>%
add_locked_out_constraints("locked_out") %>%
add_binary_decisions() %>%
add_gurobi_solver(gap = 0)
# solve problem
s <- solve(p)
## Optimize a model with 62 rows, 1130 columns and 1560 nonzeros
## Variable types: 0 continuous, 1130 integer (1130 binary)
## Coefficient statistics:
## Matrix range [1e-02, 7e-01]
## Objective range [2e-01, 6e+01]
## Bounds range [1e+00, 1e+00]
## RHS range [2e-03, 2e+00]
## Found heuristic solution: objective 9745.2
## Presolve removed 33 rows and 922 columns
## Presolve time: 0.00s
## Presolved: 29 rows, 208 columns, 380 nonzeros
## Found heuristic solution: objective 9134.1484174
## Variable types: 0 continuous, 208 integer (208 binary)
## Presolved: 29 rows, 208 columns, 380 nonzeros
##
##
## Root relaxation: objective 8.974193e+03, 40 iterations, 0.00 seconds
##
## Nodes | Current Node | Objective Bounds | Work
## Expl Unexpl | Obj Depth IntInf | Incumbent BestBd Gap | It/Node Time
##
## 0 0 8974.19273 0 18 9134.14842 8974.19273 1.75% - 0s
## H 0 0 9002.6666824 8974.19273 0.32% - 0s
## H 0 0 8997.0711748 8974.19273 0.25% - 0s
## 0 0 8989.32909 0 11 8997.07117 8989.32909 0.09% - 0s
## 0 0 8994.00517 0 19 8997.07117 8994.00517 0.03% - 0s
## 0 0 8995.60563 0 13 8997.07117 8995.60563 0.02% - 0s
## 0 0 8995.61361 0 13 8997.07117 8995.61361 0.02% - 0s
## 0 0 cutoff 0 8997.07117 8997.07117 0.00% - 0s
##
## Cutting planes:
## Gomory: 1
## Cover: 9
## Clique: 1
## MIR: 8
## StrongCG: 1
##
## Explored 1 nodes (82 simplex iterations) in 0.02 seconds
## Thread count was 1 (of 4 available processors)
##
## Solution count 4: 8997.07 9002.67 9134.15 9402.59
##
## Optimal solution found (tolerance 0.00e+00)
## Best objective 8.997071174781e+03, best bound 8.997071174781e+03, gap 0.0000%
# plot solution
spplot(s, "solution_1", col.regions = c("grey90", "#D81E36"), main = NULL,
colorkey = FALSE)
# create problem
p <- problem(tas_pu, tas_features, "cost") %>%
add_min_set_objective() %>%
add_relative_targets(0.1) %>%
add_locked_in_constraints("locked_in") %>%
add_locked_out_constraints("locked_out") %>%
add_boundary_penalties(1e-2, 0.5) %>%
add_binary_decisions() %>%
add_gurobi_solver(gap = 0)
# solve problem
s <- solve(p)
## Optimize a model with 6358 rows, 4278 columns and 14152 nonzeros
## Variable types: 0 continuous, 4278 integer (4278 binary)
## Coefficient statistics:
## Matrix range [1e-02, 1e+00]
## Objective range [1e+00, 2e+03]
## Bounds range [1e+00, 1e+00]
## RHS range [2e-03, 2e+00]
## Found heuristic solution: objective 38002.8
## Presolve removed 3264 rows and 2124 columns
## Presolve time: 0.06s
## Presolved: 3094 rows, 2154 columns, 6629 nonzeros
## Found heuristic solution: objective 33754.728311
## Variable types: 0 continuous, 2154 integer (2154 binary)
## Presolve removed 20 rows and 15 columns
## Presolved: 3074 rows, 2139 columns, 6588 nonzeros
##
##
## Root relaxation: objective 2.906009e+04, 1087 iterations, 0.09 seconds
##
## Nodes | Current Node | Objective Bounds | Work
## Expl Unexpl | Obj Depth IntInf | Incumbent BestBd Gap | It/Node Time
##
## 0 0 29060.0889 0 634 33754.7283 29060.0889 13.9% - 0s
## H 0 0 31614.195545 29060.0889 8.08% - 0s
## H 0 0 30704.847480 29060.0889 5.36% - 0s
## H 0 0 29992.088988 29060.0889 3.11% - 0s
## 0 0 29311.5879 0 515 29992.0890 29311.5879 2.27% - 0s
## 0 0 29364.2269 0 409 29992.0890 29364.2269 2.09% - 0s
## H 0 0 29729.173641 29364.2269 1.23% - 0s
## 0 0 29370.7027 0 578 29729.1736 29370.7027 1.21% - 0s
## 0 0 29372.8483 0 741 29729.1736 29372.8483 1.20% - 0s
## H 0 0 29614.708286 29372.8483 0.82% - 0s
## 0 0 29373.0489 0 740 29614.7083 29373.0489 0.82% - 0s
## 0 0 29373.6493 0 744 29614.7083 29373.6493 0.81% - 0s
## 0 0 29373.6697 0 741 29614.7083 29373.6697 0.81% - 0s
## 0 2 29373.7125 0 741 29614.7083 29373.7125 0.81% - 1s
## 545 78 29592.3975 10 67 29614.7083 29494.9796 0.40% 50.1 5s
##
## Cutting planes:
## Gomory: 4
## Cover: 16
## MIR: 16
## StrongCG: 2
## Zero half: 4
## Mod-K: 1
##
## Explored 1371 nodes (65040 simplex iterations) in 8.84 seconds
## Thread count was 1 (of 4 available processors)
##
## Solution count 7: 29614.7 29729.2 29992.1 ... 36545.2
##
## Optimal solution found (tolerance 0.00e+00)
## Best objective 2.961470828563e+04, best bound 2.961470828563e+04, gap 0.0000%
# plot solution
spplot(s, "solution_1", col.regions = c("grey90", "#D81E36"), main = NULL,
colorkey = FALSE)
# create problem
p <- problem(tas_pu, tas_features, "cost") %>%
add_min_set_objective() %>%
add_relative_targets(0.1) %>%
add_locked_in_constraints("locked_in") %>%
add_locked_out_constraints("locked_out") %>%
add_proportion_decisions() %>%
add_gurobi_solver(gap = 0)
# solve problem
s <- solve(p)
## Optimize a model with 62 rows, 1130 columns and 1560 nonzeros
## Coefficient statistics:
## Matrix range [1e-02, 7e-01]
## Objective range [2e-01, 6e+01]
## Bounds range [1e+00, 1e+00]
## RHS range [2e-03, 2e+00]
## Presolve removed 26 rows and 813 columns
## Presolve time: 0.00s
## Presolved: 36 rows, 317 columns, 498 nonzeros
##
## Iteration Objective Primal Inf. Dual Inf. Time
## 0 8.4801640e+03 7.314124e+00 0.000000e+00 0s
## 34 8.7426883e+03 0.000000e+00 0.000000e+00 0s
##
## Solved in 34 iterations and 0.00 seconds
## Optimal objective 8.742688306e+03
# plot solution
spplot(s, "solution_1", main = NULL, colorkey = TRUE)
# create problem
p <- problem(tas_pu, tas_features, "cost") %>%
add_max_utility_objective(budget) %>%
add_relative_targets(0.1) %>%
add_locked_in_constraints("locked_in") %>%
add_locked_out_constraints("locked_out") %>%
add_proportion_decisions() %>%
add_gurobi_solver(gap = 0)
# solve problem
s <- solve(p)
## Warning in compile.ConservationProblem(a, ...): ignoring targets since the
## maximum coverage objective function doesn't use targets
## Optimize a model with 63 rows, 1192 columns and 2752 nonzeros
## Coefficient statistics:
## Matrix range [1e-02, 6e+01]
## Objective range [1e-10, 1e+00]
## Bounds range [2e-02, 2e+01]
## RHS range [1e+04, 1e+04]
## Presolve removed 62 rows and 645 columns
## Presolve time: 0.01s
## Presolved: 1 rows, 547 columns, 547 nonzeros
##
## Iteration Objective Primal Inf. Dual Inf. Time
## 0 1.2564462e+02 1.063327e+02 0.000000e+00 0s
## 1 4.6246412e+01 0.000000e+00 0.000000e+00 0s
##
## Solved in 1 iterations and 0.01 seconds
## Optimal objective 4.624641160e+01
# plot solution
spplot(s, "solution_1", main = NULL, colorkey = TRUE)
# create problem
p <- problem(tas_pu, tas_features, "cost") %>%
add_max_features_objective(budget) %>%
add_relative_targets(0.1) %>%
add_locked_in_constraints("locked_in") %>%
add_locked_out_constraints("locked_out") %>%
add_proportion_decisions() %>%
add_gurobi_solver(gap = 0)
# solve problem
s <- solve(p)
## Warning for adding variables: zero or small (< 1e-13) coefficients, ignored
## Optimize a model with 63 rows, 1192 columns and 2751 nonzeros
## Variable types: 1130 continuous, 62 integer (62 binary)
## Coefficient statistics:
## Matrix range [2e-03, 6e+01]
## Objective range [1e-10, 1e+00]
## Bounds range [1e+00, 1e+00]
## RHS range [1e+04, 1e+04]
## Found heuristic solution: objective 35
## Presolve removed 25 rows and 836 columns
## Presolve time: 0.00s
## Presolved: 38 rows, 356 columns, 855 nonzeros
## Variable types: 319 continuous, 37 integer (37 binary)
## Presolved: 38 rows, 356 columns, 855 nonzeros
##
##
## Root relaxation: objective 6.200001e+01, 29 iterations, 0.01 seconds
##
## Nodes | Current Node | Objective Bounds | Work
## Expl Unexpl | Obj Depth IntInf | Incumbent BestBd Gap | It/Node Time
##
## * 0 0 0 62.0000054 62.00001 0.00% - 0s
##
## Explored 0 nodes (29 simplex iterations) in 0.02 seconds
## Thread count was 1 (of 4 available processors)
##
## Solution count 2: 62 35
##
## Optimal solution found (tolerance 0.00e+00)
## Best objective 6.200000543877e+01, best bound 6.200000543877e+01, gap 0.0000%
# plot solution
spplot(s, "solution_1", main = NULL, colorkey = TRUE)
